3. (30 pts) Consider a long tube, insulated at the outer radius r, and cooled at...

 

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3. (30 pts) Consider a long tube, insulated at the outer radius r, and cooled at the inner radius ri, with uniform heat generation (W/m) within the solid. conv To, h To a. k Insulation Coolant Th a) List all appropriate assumptions, simplify the DOE to get the governing equation, and obtain the general solution (still keep the integration constants) for the temperature distribution in the tube. b) In a practical application a limit would be placed on the maximum temperature that is permissible at the insulated surface (r). Specifying the limit as To, identify appropriate boundary conditions that could be used to determine the arbitrary constants appearing in the general solution. Determine these constants and the corresponding form of the temperature distribution. Hint: there is no heat loss at the outer surface of the tube because of the insulation. 3. (30 pts) Consider a long tube, insulated at the outer radius r, and cooled at the inner radius ri, with uniform heat generation (W/m) within the solid. conv To, h To a. k Insulation Coolant Th a) List all appropriate assumptions, simplify the DOE to get the governing equation, and obtain the general solution (still keep the integration constants) for the temperature distribution in the tube. b) In a practical application a limit would be placed on the maximum temperature that is permissible at the insulated surface (r). Specifying the limit as To, identify appropriate boundary conditions that could be used to determine the arbitrary constants appearing in the general solution. Determine these constants and the corresponding form of the temperature distribution. Hint: there is no heat loss at the outer surface of the tube because of the insulation.